Fuzzy Interpolative Reasoning Method Based on Spline

Abstract

When rule base is sparse and an observation is in the gap between two neighboring antecedences, we cannot get a satisfactory reasoning result by traditional fuzzy reasoning method. Fuzzy reasoning is really an interpolation. For only using two neighboring rules, classical KH linear interpolative reasoning method is partial and its consequence does not always preserve convexity and normality. This paper presents a non-linear fuzzy interpolative method based on B-spline. Definitions of fuzzy setpsilas core set, left core, right core, center core, left width, middle width and right width are given. The method includes two steps. First confirm the core of result fuzzy sets, and then confirm the shape of result fuzzy sets. The method can not only handle one dimension and multidimensional fuzzy reasoning but also preserve the convexity and normality of reasoning consequence. Two class simulation instances are given.